The set of all points where the function f(x)=x+|x| is differentiable, is
(a) (0,∞) (b) (-∞,0)
(c) (-∞,0)∪(0,∞) (d) (-∞,∞)
This question is similar to Question-15 NCERT-Exemplar-MCQs
CBSE Class 12 Sample Paper for 2024 Boards
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CBSE Class 12 Sample Paper for 2024 Boards
Last updated at April 16, 2024 by Teachoo
This question is similar to Question-15 NCERT-Exemplar-MCQs
๐(๐ฅ) = ๐ฅ+|๐ฅ| = {โ(๐ฅ+๐ฅ, ๐ฅโฅ0@๐ฅโ๐ฅ, ๐ฅ <0)โค = {โ(2๐ฅ, ๐ฅโฅ0@0, ๐ฅ<0)โค Now, f(x) is a differentiable at x = 0 if LHD = RHD (๐๐๐)โฌ(๐กโ๐) (๐(๐) โ ๐(๐ โ ๐))/๐ = (๐๐๐)โฌ(hโ0) (๐(0) โ ๐(0 โ โ))/โ = (๐๐๐)โฌ(๐กโ๐) (๐(๐) โ ๐(โ๐))/๐ =(๐๐๐)โฌ(โโ0) (2(0) โ 0)/โ = (๐๐๐)โฌ(hโ0) 0/โ = ๐ (๐๐๐)โฌ(๐กโ๐) (๐(๐ + ๐) โ ๐(๐ ))/๐ = (๐๐๐)โฌ(hโ0) (๐(0 + โ) โ ๐(0))/โ = (๐๐๐)โฌ(๐กโ๐) (๐(๐) โ ๐(๐))/๐ = (๐๐๐)โฌ(hโ0) (2โ โ 0)/โ = (๐๐๐)โฌ(hโ0) 2โ/โ = ๐ Hence, we can say that f(x) is differentiable on R โ {๐} or (โโ,๐)โช(๐,โ) So, the correct answer is (c)